Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. The combined cost of three articles in a shop is Rs.4200. Two article sold at profit of 25% and 12.5% and third article is sold such that there is a loss of Rs.630. What is the loss percentage incurred on third article. I. The difference between cost price of highest article and lowest article is Rs.600. The costliest article is sold at a loss.  II, The cheapest item is sold at 25% profit. The the price of one of that article is the average price of the cheapest and costliest item.

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. The combined cost of three articles in a shop is Rs.4200. Two article sold at profit of 25% and 12.5% and third article is sold such that there is a loss of Rs.630. What is the loss percentage incurred on third article. I. The difference between cost price of highest article and lowest article is Rs.600. The costliest article is sold at a loss.  II, The cheapest item is sold at 25% profit. The the price of one of that article is the average price of the cheapest and costliest item. Correct Answer If the data in both statements I and II together are needed to answer the question.

Cost price of the articles = Rs.4200

Selling price of the articles = 4200 – 630 = Rs.3570 

Using statement I

Let the cost price of the cheapest article be x

Then, the cost price of the costliest article be x + 600

∴ Cost price of third article = 4200 – x – (x + 600) = 3600 – 2x

Statement I alone is not sufficient to answer the question

Using statement II

Let the price of the cheapest item and the costliest item be x and y respectively

Then, the cost price of third item = (x + y)/2

∴ Selling price of the articles = x × (125/100) + {(x + y)/2} × 9/8 + y × (z/100)      ----(12.5% = 1/8)

where z → loss percentage

Statement II alone is not sufficient to answer the question 

Using statement I and statement II together 

The cost price of the third article is the avg of the cost price of cheapest and costliest article

∴ (x + x + 600)/2 = 3600 – 2x

⇒ x + 300 = 3600 – 2x

⇒ x = 1100

Cost price of cheapest article = 1100

Cost price of costliest article = 1100 + 600 = 1700

Cost price of third article = (1100 + 1700)/2 = 1400

Selling price of the articles = 1100 × (125/100) + 1400 × 9/8 + 1700 × (z/100)

⇒ 3570 = 1375 + 1575 + 17z

⇒ 620 = 17z  

⇒ z = 36.47%

∴ Loss % = 100 – 36.47 = 64.53%

∴ The data in both statements I and II together are needed to answer the question.